Tutte showed in [1]} that various polynomials and invariants, including the adjacency characteristic polynomial and chromatic polynomial of a graph, are reconstructible. It turns out that the combinatorial Laplacian characteristic polynomial is also reconstructible, because the \(U\) -polynomial is reconstructible, e.g. by considering the spanning subgraph expansion of the \(U\) -polynomial in [2]}, and applying [1]} and [1]} to reconstruct the terms corresponding to the disconnected and connected spanning subgraphs, respectively.

